Lie Groups, An Approach through Invariants and Representations


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Asked 9 years, 11 months ago. Active 9 years, 2 months ago. Viewed 4k times. It is very interesting, starts off with some things including a section about strata, and then in the core of the book has two constructions to get these quotients. If you are interested in homology of the spaces constructed in GIT, maybe the following paper by Woolf is very helpful: arxiv.

Feb 27 '10 at Andrea Ferretti Andrea Ferretti 8, 8 8 gold badges 62 62 silver badges bronze badges. For the classical-groups-and-rings treatment using algebra, books by Goodman-Wallach and Procesi I cited in another comment are thorough and readable. An approach through invariants and representations which provides an excellent update on both Weyl's "Classical groups.

Jordan-Kronecker invariants of finite-dimensional Lie algebras

Their invariants and representations" and the relevant parts of Hodge and Pedoe's "Methods of algebraic geometry", I'd like to mention an amazing book by Kraft, unortunately not translated into English yet there is a Russian translation : Kraft, Geometrische Methoden in der Invariantentheorie For a bird's eye view, I recommend the following survey in Russian Yellow Springer Math Encyclopaedia: Vinberg and Popov, Invariant theory , Algebraic geometry IV.

Victor Protsak Victor Protsak Jim Humphreys Vinoth Vinoth 13 13 silver badges 35 35 bronze badges. Graduate Texts in Mathematics, Springer, Dordrecht, Second edition of book mentioned. An approach through invariants and representations.

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Springer, New York, Andreas Holmstrom Andreas Holmstrom 3, 3 3 gold badges 26 26 silver badges 53 53 bronze badges. Abdelmalek Abdesselam Abdelmalek Abdesselam If anything, classical invariant theory that I am familiar with is closer to modern representation theory than to algebraic geometry. Some of the key players like Clebsch, Cayley, Sylvester, In fact, CIT as practiced by the classics is inseparable from elimination theory. Maybe a good way to see this would be to look at the two books by Faa di Bruno available on google books: the one on binary forms, and the one on elimiation theory.

See also Gordan's papers on symbolic forms of resultants.

Special Functions and Their Symmetries

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Lie groups has been an increasing area of focus and research since the middle of the 20th century. This title gives the reader a comprehensive treatment of the classical Lie groups along with an introduction to a range of topics associated with Lie groups such as: symmetric functions, theory of algebraic forms, Lie algebras, and more. While every attempt has been made to ensure stock availability, occasionally we do run out of stock at our stores.

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Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations Lie Groups, An Approach through Invariants and Representations
Lie Groups, An Approach through Invariants and Representations

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